I have come across a card with an earlier postmark to one given in the database. While it is difficult to make out the day the postmark is July 1904. The day is1?, my guess was possibly 14.
The card is on EBay and the link is PC68133 Runswick Bay. Yorks. Tuck. Oilette. No 1668. 1904 for sale | eBay
The image is:
@PhilW nice one, I’ve uploaded the back to this card:
https://tuckdbpostcards.org/items/112112
Yeah I guess it’s 1914…
It looks like other cards in that set are published 1904, so I’ll leave the earlier date.